On the Free Loop Space of Homogeneous Spaces
Copyright policy )On the Free Loop Space of Homogeneous Spaces
This paper shows that if M is a compact simply connected homogeneous space which is not diffeomorhic to a symmetric space of rank one, then the Betti numbers with \({\mathbb{Z}}_ 2\)-coefficients of the free loop space of M are unbounded. As a corollary, the authors extend a result of Gromoll-Meyer to show that any Riemannian metric on M has infinitely many geometrically different closed geodesics.
Betti numbers of the free loop space, compact simply connected homogeneous space, infinitely many geometrically different closed geodesics, Differential geometry of homogeneous manifolds, Homology and cohomology of \(H\)-spaces, symmetric space of rank one, Geodesics in global differential geometry, Loop spaces
Betti numbers of the free loop space, compact simply connected homogeneous space, infinitely many geometrically different closed geodesics, Differential geometry of homogeneous manifolds, Homology and cohomology of \(H\)-spaces, symmetric space of rank one, Geodesics in global differential geometry, Loop spaces
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